More explicitly, as shown in figure REF (b), one can construct two kinds of tensors using thread/state correspondence, denoted as \(V\)  and \(W\) . Wherein \(V\)  represents the distillation tensor [1]}, [2]}, [3]}, which is defined as mapping the reduced state of each boundary elementary region to the SS state associated with its RT surface. In this paper, we do not focus on the study of \(V\)  tensor, which is merely a pro forma definition at the moment. The \(W\)  tensor plays the role of a \(disentangler\)  [4]}, [5]}, [6]}, [7]}, which maps the SS states of the two RT surfaces in the previous layer to the SS state of the RT surface in the next layer.
Notice in the figure we also assign an arrow direction to each leg to specify the upper and lower indices of a tensor, then we can first write the \(W\)  tensor as \(W_{\mu \nu }^\lambda \)  pro forma, where \(\mu \)  and \(\nu \)  represent the SS states of the two RT surfaces of the previous layer, respectively, while \(\lambda \)  represents the SS state of the RT surface of the inner layer. Then the thread/state correspondence indicates that \(\mu \) , \(\nu \)  and \(\lambda \)  could be further decomposed into smaller indices, thus one can write a universal expression for the \(W\)  tensor of any layer immediately. We first write down the corresponding pure state of the closed surface that is the boundary of the cell of each layer. Consider a cell consisting of three RT surfaces \({\gamma _R}\) , \({\gamma _S}\)  and \({\gamma _T}\)  corresponding to three adjacent composite boundary regions \(R\) , \(S\)  and \(T\) , respectively. Let us denote \(R = \cup {A_r}\) , \(S = \cup {A_s}\) , \(T = \cup {A_t}\) , i.e., denote the elementary regions within \(R\) , \(S\)  and \(T\)  as \({A_r}\) , \({A_s}\)  and \({A_t}\)  respectively. Following these notations, we can write:

\(\begin{array}{l}\left| {{\Psi _{{\gamma _R} \cup {\gamma _S} \cup {\gamma _T}}}} \right\rangle = \left( {\sum \limits _{r,t} {\sum \limits _{{q_{rt}} = 0}^{{2^{{F_{rt}}}} - 1} {} } } \right)\left( {\sum \limits _{s,t} {\sum \limits _{{q_{st}} = 0}^{{2^{{F_{st}}}} - 1} {} } } \right)\left( {\sum \limits _{r,s} {\sum \limits _{{q_{rs}} = 0}^{{2^{{F_{rs}}}} - 1} {} } } \right)\\\frac{1}{{\sqrt{{2^{\sum \limits _{r,t} {{F_{rt}}} + \sum \limits _{s,t} {{F_{st}}} + \sum \limits _{r,s} {{F_{rs}}} }}} }} \cdot \left( {\prod \limits _{r,t} {\left| {{\phi _{rt}} = {q_{rt}}} \right\rangle } } \right)\\\otimes \left( {\prod \limits _{s,t} {\left| {{\phi _{st}} = {q_{st}}} \right\rangle } } \right) \otimes \left( {\prod \limits _{r,s} {\left| {{\phi _{rs}} = {q_{rs}}} \right\rangle } } \right)\end{array},\) 
